# [SOLVED] Algebra (Cumulative Review) Linear Systems and Inequalities

• Apr 28th 2008, 06:22 PM
jscalalamoboy
[SOLVED] Algebra (Cumulative Review) Linear Systems and Inequalities
Ok, I have no clue how to do these, its a linear inequality system.

{y≤1/5x+12/5
{y≥-x
{y≥2x-3
Btw, they are all in one bracket. How do I write equations?
• Apr 28th 2008, 08:36 PM
Soroban
Hello, jscalalamoboy!

No clue ??

Okay, just this once . . . for you . . .

Quote:

$\begin{Bmatrix}y \:\leq \:\frac{1}{5}x + \frac{12}{5} \\
y \:\geq \:-x \\ y\:\geq\:x-3 \end{Bmatrix}$

You need to graph the inequalities and shade the required region.

Graph the line: . $y \:=\:\frac{1}{5}x + \frac{12}{5}$
. . . It has y-intercept $\frac{12}{5}$ and slope $\frac{1}{5}$

The inequality is $\leq$ . . . Shade the region below the line.
Code:

                |                  *;;                 |              *:::::;                 |          *::::::::                 |      *::::::::::                 |  *::::::::::::                 *::::::::::::::             *:::|::::::::::::         *:::::::|::::::::::   - *:-:-:-:-:-:+:-:-:-:- - - - - - -     ::::::::::::|::::::     ::::::::::::|::::                 |

Graph the line: . $y \:=\:-x$
. . It has y -intercept 0 and slope -1.

The inequality is $\geq$ . . . Shade the region above the line.
Code:

    *:::::::::::|:::       *:::::::::|::::         *:::::::|:::::           *:::::|::::::             *:::|:::::::               *:|::::::::     - - - - - - *:-:-:-:-:- -                 | *::::::::                 |  *:::::::                 |    *::::::                 |      *                 |

Graph the line: . $y \:=\:2x-3$
. . It has y-intercept -3 and slope 2.

The inequality is $\geq$ . . . Shade the region above the line.
Code:

                |:::::::::::*                 |::::::::::*               :|:::::::::*               ::|::::::::*             :::|:::::::*             ::::|::::::*     - - - -:-:-:+:-:-:* - - -           ::::::|::::*         :::::::|:::*         ::::::::|::*       :::::::::|:*       ::::::::::|

The solution is the triangular region common to all three.
And we are usually expected to find the coordinates of the vertices.
Code:

                |                 |          o(3,3)                 |      *::*                 |  *:::::*                 *::::::::*       (-2,2)o:::|:::::::*               *:|::::::* - - - - - - - - *:-:-:* - - - - - - -                 | *::*                 |  o(1,-1)                 |
• Apr 28th 2008, 08:55 PM
elizsimca
how do you do those fun graphs soroban?
• Apr 29th 2008, 09:33 PM
jscalalamoboy
(Rock)YEAH! Thanks bro! I PASSED! WHOOOOOO!